Abstract

A scalar conservation law ut +div (u) = f is considered with the initial datum u|t=0 = u0 2 L1 loc(RN) and f 2 L1loc(RN ×(0, T)) only. In this case the classical Krushkov condition can make no sense because of unboundedness of u, if no growth condition on is assumed. This obstacleis overcome by introducing the so-called renormalized entropy solution generalizing the classical one. Existence and uniqueness of such a solution is established.